Mining giant Anglo American is poised to ask the City Takeover Panel to issue Xstrata with a "put up or shut up" order, which will force it to bid for Anglo within a set time frame or walk away for at least six months.

The new chairman of Anglo, Sir John Parker, has widespread investor support for the move after concluding a series of talks with its leading shareholders in Britain, South Africa and the US.

Parker, who is also chairman of National Grid and head of Mondi, the South African paper manufacturer, is determined to bring clarity to the situation after Xstrata made a proposal for a nil premium merger in June, which was rejected by the Anglo board.

Xstrata is under pressure to increase the value of its bid, which would have created a company worth £40bn in a deal that Xstrata chief executive Mick Davis contends is both fair and reasonable.

Under takeover panel rules, a company being besieged by another can ask for the bidder to put a firm offer on the table or withdraw. Two months ago, Xstrata made public a letter to Anglo in which it suggested the two join forces in a so-called "merger of equals" – a move that could yield $1bn of cost savings. But it was rejected by Parker's predecessor, Mark Moody-Stuart, on the grounds that it undervalued Anglo, most of whose operations are in southern Africa.

Anglo's City shareholders, while not against a takeover in principle, are pushing for a higher offer from Davis, possibly one that could include a £6bn-£10bn cash component. Investors believe Anglo should demand a premium on the grounds that its assets are superior to those of Xstrata, the smaller of the two companies.

However, Davis is viewed by some investors as a better manager than Anglo's chief executive Cynthia Carroll. She has been criticised for buying assets at the top of the market and for cutting the dividend earlier this year.

But Carroll's cost-cutting drive is now producing results and she has received the backing of Parker who said he was "very happy" with the plans that Carroll has put forward for "cost reduction and value creation". "She has done some outstanding transformational work," Parker said at his appointment in July.

Analysts caution that Xstrata may not have the financial headroom to improve on its original terms as its net debt stands at $13bn, although it could seek to raise funds from its shareholders.

Separately, Parker has ordered Anglo's managers to accelerate plans for asset disposals – including the sale of British construction firm Tarmac. Parker is keen to make disposals to bolster the balance sheet and pave the way for a return to dividend payments.